Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves of frequency f, and we assume that the blood cells are moving directly toward the ultrasound source, show that the frequency (r of reflected waves detected by the apparatus is given by

There are two Doppler shifts. A red blood cell first acts as a moving observer; then it acts as a moving source when it reradiates the reflected sound at the same frequency that it received.

f1+ vlu f =1- olu